Question

The perimeter of a rectangular garden is 196 m. Its length is  5m more than twice its breadth. What are the length and the breadth of the garden ?​

Answer 1

Given :

• The perimeter of a rectangular garden is 196 m.
• Length is  5m more than twice its breadth.

To Find :

• Length and Breadth of Garden .

Solution :

$\longmapsto\tt{Let\:Breadth\:be=x}$

As Given that Length is  5m more than twice its breadth. So ,

$\longmapsto\tt{Length=2x+5}$

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Rectangle=2(l+b)}$

Putting Values :

$\longmapsto\tt{196=2(2x+5+x)}$

$\longmapsto\tt{\cancel\dfrac{196}{2}=3x+5}$

$\longmapsto\tt{98-5=3x}$

$\longmapsto\tt{93=3x}$

$\longmapsto\tt{\cancel\dfrac{93}{3}=x}$

$\longmapsto\tt\bf{31=x}$

Value of x is 31 .

Therefore :

$\longmapsto\tt{Breadth\:of\:Garden=x}$

$\longmapsto\tt\bf{31\:m}$

$\longmapsto\tt{Length\:of\:Garden=2(31)+5}$

$\longmapsto\tt\bf{67\:m}$

Answer 2

Given :

The perimeter of a rectangular garden is 196 m. Its length is  5m more than twice its breadth. What are the length and the breadth of the garden ?

How To Solve :

• First we need to take any variable to get the breadth. The same variable will be applied in case of Length as well because they are inter-related to each other. Let us assume it as B after which the length becomes 2B + 5. Applying the formula of Perimeter we'll put their respective values and get B. From B we can get the breadth and putting B's value in 2B + 5 we can get the length

Solution :

Let us assume :

The breadth be B

According to the question,

Length is 2 times the breadth and 5 m more

So, we get the length to be 2B + 5 m

Given that :

Perimeter = 196 m

Formula for the Perimeter of the Rectangle :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \pink{ \underline{ \overline{\blue{ \boxed{ \green{ \frak{ {\sf P}erimeter_{(Rectangle)} = 2(Length + Breadth)}}}}}}}$

Putting the values in the formula we get

$\twoheadrightarrow \purple{{ \frak{196 \: m = 2(2B + 5 \: m + B)}}}$

$\twoheadrightarrow \purple{{ \frak{196 \: m = 2(3B + 5 \:m )}}}$

$\twoheadrightarrow \purple{\frak{196 = 6B + 10 \: m}}$

Transposing 10m to the other side we get -10m

$\twoheadrightarrow \purple{ \frak{196 \: m - 10 \: m = 6B}}$

$\twoheadrightarrow\purple{\frak{6B = 186 \: m}}$

By cross multiplying we get

$\twoheadrightarrow\purple{\frak{B = \frac{186}{6} \: m}}$

$\twoheadrightarrow\purple{\frak{B = \cancel{ \frac{186}{6} \: m }}}$

$\star \: \orange{ \underline{ \boxed{ \pink{\frak{B=31 \: m}}}}}$

_____________________________

Now, finding the breadth and the length

Breadth = B = 31 m

Length = 2B + 5 m

• 2(31 m) + 5 m

• 62 m + 5 m

• 67 m

☞ The Breadth is 31 m whereas the Length is 67 m

Verification :

• Perimeter = 2(Length + Breadth)

• 196 m = 2(31 m + 67 m)

• 196 m = 2(98 m)

• 196 m = 196 m

Hence, Verified !!